Phase transition and Martin boundary
Phase transition for the frog model.
Phase-type distributions and perturbation model
Phénomène de cutoff pour certaines marches aléatoires sur le groupe symétrique
The main purpose of this paper is to exhibit the cutoff phenomenon, studied by Aldous and Diaconis [AD]. Let denote a transition kernel after k steps and π be a stationary measure. We have to find a critical value for which the total variation norm between and π stays very close to 1 for , and falls rapidly to a value close to 0 for with a fall-off phase much shorter than . According to the work of Diaconis and Shahshahani [DS], one can naturally conjecture, for a conjugacy class with...
Philosophischer Versuch über die Wahrscheinlichkeiten [Book]
Physical measures for infinite-modal maps
We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they satisfy the...
Phytoplankton Dynamics: from the Behavior of Cells to a Transport Equation
We present models of the dynamics of phytoplankton aggregates. We start with an individual-based model in which aggregates can grow, divide, joint and move randomly. Passing to infinity with the number of individuals, we obtain a model which describes the space-size distribution of aggregates. The density distribution function satisfies a non-linear transport equation, which contains terms responsible for the growth of phytoplankton aggregates, their fragmentation, coagulation, and diffusion.
Piecewise Markov processes in discrete time and their certain extensions
Piecewise Markov processes on a general state space
Pierre-Simon de Laplace a inverzní pravděpodobnost
Pitman's theorem for skip-free random walks with Markovian increments.
Planar anisotropy revisited
The paper concerns estimation of anisotropy of planar fibre systems using the relation between the rose of directions and the rose of intersections. The discussion about the properties of the Steiner compact estimator is based on both theoretical and simulation results. The approach based on the distribution of the Prokhorov distance between the estimated and true rose of directions is developed. Finally the curved test systems are investigated in both Fourier and Steiner compact analysis of anisotropy....
Planar Lorentz process in a random scenery
We consider the periodic planar Lorentz process with convex obstacles (and with finite horizon). In this model, a point particle moves freely with elastic reflection at the fixed convex obstacles. The random scenery is given by a sequence of independent, identically distributed, centered random variables with finite and non-null variance. To each obstacle, we associate one of these random variables. We suppose that each time the particle hits an obstacle, it wins the amount given by the random variable...
Planar semimartingales obtained by transformations of two-parameter martingales
Plongement de lois indéfiniment divisibles
Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory
This paper deals with the problem of estimating the level sets L(c) = {F(x) ≥ c}, with c ∈ (0,1), of an unknown distribution function F on ℝ+2. A plug-in approach is followed. That is, given a consistent estimator Fn of F, we estimate L(c) by Ln(c) = {Fn(x) ≥ c}. In our setting, non-compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by...
Plug-in estimators for higher-order transition densities in autoregression
In this paper we obtain root-n consistency and functional central limit theorems in weighted L1-spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based kernel estimator....
Plurisubharmonic martingales and barriers in complex quasi-Banach spaces
We describe the geometrical structure on a complex quasi-Banach space that is necessay and sufficient for the existence of boundary limits for bounded, -valued analytic functions on the open unit disc of the complex plane. It is shown that in such spaces, closed bounded subsets have many plurisubharmonic barriers and that bounded upper semi-continuous functions on these sets have arbitrarily small plurisubharmonic perturbations that attain their maximum. This yields a certain representation of...
Počátky počtu pravděpodobnosti [Book]
Počet pravděpodobnosti v geometrii